Magneto-thermo-viscoelastic interactions in an unbounded body with a spherical cavity subjected to a periodic loading (Q1883163)

The paper deals with the generation of stress, temperature and magnetic field in an unbounded isotropic homogeneous viscoelastic medium with a spherical cavity placed in a constant primary magnetic field. It is an extension of the paper [\textit{S. Mukhopadhyay}, J. Thermal Stresses, 23, 675--684 (2000)] so as to include the effect of the magnetic field. The medium is a perfect electric conductor, and its response in the elastic range is taken to be a Voigt type of linear viscoelastic model. The interaction of the coupled electromagnetic, thermal and viscoelastic fields is investigated for the medium under a periodic mechanical loading on the boundary of the cavity. A generalised thermoelasticity theory for Kelvin-Voigt material by \textit{A. E. Green} and \textit{K. A. Lindsay} [J. Elasticity, 2, 1-7 (1972; Zbl 0775.73063)] is used, including the effect of second sound. The solutions for the displacement, temperature and stresses are obtained in terms of spherical Hankel functions. Numerical results are reported for radial variations of displacements, stresses, temperature, and for the relaxation times and the magnetic field of copper as a magneto-thermo-viscoelastic material. Noteworthy is that the effect of the thermal relaxation is very small in most of engineering materials. Therefore, the effect is in need of further modification and experimental corroboration before including it in any study.